# Question #27abc

Feb 24, 2017

The vertex is at $\left(1 , - 6\right)$

#### Explanation:

There are different methods you can use.

A quadratic has the form $a {x}^{2} + b x + c$

$y = {x}^{2} - 2 x - 5$ is the equation of a parabola.

The vertex lies on the line of symmetry of the parabola.
It is a vertical line and can be found from $x = \frac{- b}{2 a}$

Once you know the $x$-value, substitute it into the equation of the parabola to find the $y$-value.

$x = \frac{- b}{2 a} = \frac{- \left(- 2\right)}{2 \left(1\right)} = \frac{2}{2} = 1$

Now find $y$

$y = {x}^{2} - 2 x - 5 = {\left(1\right)}^{2} - 2 \left(1\right) - 5 = - 6$

The vertex is at $\left(1 , - 6\right)$

OR:
Completing the square will give the vertex form.

OR:
You can draw the graph by finding points and plotting them and then read the vertex from the points or from the graph.

graph{y=x^2-2x-5 [-9.9, 10.1, -6.56, 3.44]}